Yeah, buddy, they're like magic hardware. Even if they aren't ASIC-competitive for the best ASIC's. Still magic with a market share and diverse applications that shows it. :)
FPGA's are cheap and good enough for prototyping; once one has a working VHDL / Verilog code, it's tapeout time.
Now, for remote attacks, you can embed RF circuitry in them that listens to any of that. You can embed circuits that receive incoming command, then dump its SRAM contents. You might modify the I/O circuitry to recognize a trapdoor command that runs incoming data as privileged instructions. You can put a microcontroller in there connected to PCI to do the same for host PC attacks. I know, that would be first option but I was having too much fun with RTL and transistor level. :)